Brent,
It sounds like you are saying that probability is useful because it
allows us to predict things-- we convert (past) relative frequencies
to (future) subjective beliefs. This cannot be denied. But I don't
feel like it answers very much... to understand what t means to
"predict", I need to understand time already, which is what is being
questioned here... What does it mean for a prediction to be more or
less reasonable, if all possible futures in fact occur? How does it
help me to take the past experimental frequencies, if I know (or at
least believe) that all alternatives will take place?
>> Mathematically, though, a real-values time variable doesn't eliminate
>> moments, it just makes an infinite number of them between any other
>> two, with a particular mathematical structure. So the question of what
>> makes them "stick together" remains.
>>
> They come with a topology which is about the only concept of sticking
> together I can imagine.
So anything with a topology counts as time?? That doesn't sound right.
Or are you saying it is necessary, rather then sufficient?
--Abram
On Sat, Dec 20, 2008 at 12:54 AM, Brent Meeker <meekerdb.domain.name.hidden> wrote:
>
> Abram Demski wrote:
>> Brent,
>>
>> I'm not sure how the comment about real numbers effects my basic
>> argument. One interesting objection I got from someone not on this
>> list was that time isn't composed of moments at all, only intervals--
>> a "moment" is an imaginary thing that we get by considering
>> arbitrarily small intervals.
>>
> This is the same as assuming reals. Real numbers can be defined in
> terms of intervals marked by rationals
>
> http://planetmath.org/encyclopedia/DedekindCuts.html
>
>> Mathematically, though, a real-values time variable doesn't eliminate
>> moments, it just makes an infinite number of them between any other
>> two, with a particular mathematical structure. So the question of what
>> makes them "stick together" remains.
>>
> They come with a topology which is about the only concept of sticking
> together I can imagine.
>
>
>> Obviously, one reason I think that I am traveling through time is
>> because I remember the past (but can only guess at the future). But
>> "remembering the past" is an experience that takes time, spanning many
>> moments, making this a little tangled. The multiverse complicates
>> things further: even supposing that only the possible worlds implied
>> by quantum mechanics exist (that is, no alternative physics, just all
>> possible quantum states) it is quite possible for me to remember the
>> future. It's merely improbable. But if all possible alternatives
>> actually occur, I don't know what probability means. (Even if there
>> are literally more alternatives down the probable paths, does this
>> make it more probable that I experience the more probable result? What
>> would that mean?)
>>
> I think probability is useful because it has different interpretations,
> relative frequency, degree of rational belief, measure, propensity,
> etc. So you may estimate the propensity of throwing snake eyes by
> throwing many trials (relative frequency) and then base you bets on the
> results (degree of rational belief). So in the case of QM you can look
> at the Born rule as defining a measure and then reinterpret it as a
> degree of rational belief in order to inform your decisions. The
> problem is that the Born rule seems to still have to be adopted as a
> separate axiom, thus reintroducing the problem Everett intended to solve.
>
> Brent
>> --Abram
>>
>> On Thu, Dec 18, 2008 at 7:21 PM, Brent Meeker <meekerdb.domain.name.hidden> wrote:
>>
>>> Abram Demski wrote:
>>>
>>>> [Sorry if this is a duplicate, I think that I did not send correctly
>>>> the first time.]
>>>>
>>>> Bruno, everyone,
>>>>
>>>> I've decided that it will be more productive/entertaining to post my
>>>> various concerns as a new topic.
>>>>
>>>> What is time?
>>>>
>>>>
>>> Time is what you read on a clock.
>>>
>>>> I'm going to ask a bunch of questions; for the sake of brevity, I'm
>>>> going to skip my arguments (which would mostly be reasons why
>>>> particular answers don't work). I'll argue once someone replies.
>>>>
>>>> If all possible universes exist, does that mean every possible moment,
>>>>
>>>>
>>> What do you mean by "possible"? Do you mean nomologically possible -
>>> which might be very restrictive but we don't know? Or do you mean
>>> logically possible - just not instantiating a contradiction "X and
>>> not-X"? Or something inbetween?
>>>
>>>
>>>> or every possible timeline of moments? If "moments" is the answer,
>>>> then how are the moments connected?
>>>>
>>> If time is a real variable (which QM assumes), moments automatically
>>> inherit the topology of the reals.
>>>
>>>
>>>> How would it matter, since the
>>>> moments already are what they are? If "timeline" is the answer, then
>>>> there is a similar question of how it matters.
>>>>
>>>> If there is a physical universe, then is there some sort of basic
>>>> physical connection behind time?
>>>>
>>>> If the universe is mathematical in nature, then what is the
>>>> mathematical connection between moments? What sort of mathematical
>>>> connection counts as time?
>>>>
>>>> If (as was recently suggested, in connection with relativity) time
>>>> cannot really be divided into individual moments, then what is it?
>>>>
>>>>
>>> In physics, it's a variable in the equations that determines the causal
>>> topology.
>>>
>>>> Why do we experience time passing?
>>>>
>>>> Is it legitimate to think as if the next moment we experience will be
>>>> chosen randomly in some sense? Does probability or randomness have a
>>>> role to play in the flow of time?
>>>>
>>>>
>>> Randomness would seem to give a sense to the direction of time. That's
>>> why physicist who are loathe to give up time-symmetry in their equations
>>> tend to favor Everett's interpretation of QM.
>>>
>>>
>>>> In connection with UDA: what is the meaning of a first-person
>>>> probability due to uncertainty of the future? Is there any sense in
>>>> which such estimates can be more or less accurate if all possible next
>>>> moments do in fact occur?
>>>>
>>>>
>>> Good question. It's the same as asking how the Born rule arises in
>>> Everett's interpretation of QM.
>>>
>>> Brent
>>>
>>>
>>>> Hope that sparks some thought...
>>>>
>>>> --
>>>> Abram Demski
>>>> Public address: abram-demski.domain.name.hidden
>>>> Public archive: http://groups.google.com/group/abram-demski
>>>> Private address: abramdemski.domain.name.hidden
>>>>
>>>>
>>>>
>>>
>>
>>
>>
>>
>
>
> >
>
--
Abram Demski
Public address: abram-demski.domain.name.hidden
Public archive: http://groups.google.com/group/abram-demski
Private address: abramdemski.domain.name.hidden
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Received on Sat Dec 20 2008 - 23:43:50 PST